Modernize NK_baseline.mod
Johannes Pfeifer
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c48542c3f3
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@ -29,11 +29,10 @@
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*
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* Please note that the following copyright notice only applies to this Dynare
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* implementation of the model.
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*/
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/*
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* Copyright (C) 2013-2016 Dynare Team
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* Copyright (C) 2013-2020 Dynare Team
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*
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* This file is part of Dynare.
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*
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@ -51,72 +50,78 @@
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* along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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*/
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var d //preference shock
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c //consumption
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mu_z //trend growth rate of the economy (from neutral and investment specific technology)
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mu_I //growth rate of investment-specific technology growth
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mu_A //growth rate of neutral technology
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lambda //Lagrange multiplier
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R //Nominal Interest rate
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PI //Inflation
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r //rental rate of capital
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x //investment
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u //capacity utilization
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q //Tobin's marginal q
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f //variable for recursive formulation of wage setting
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ld //aggregate labor demand
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w //real wage
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wstar //optimal real wage
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PIstarw //optimal wage inflation
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PIstar //optimal price inflation
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g1 //variable 1 for recursive formulation of price setting
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g2 //variable 2 for recursive formulation of price setting
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yd //aggregate output
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mc //marginal costs
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k //capital
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vp //price dispersion term
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vw //wage dispersion term
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l //aggregate labor bundle
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phi //labor disutility shock
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F; //firm profits
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var d (long_name='preference shock')
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c (long_name='consumption')
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mu_z (long_name='trend growth rate of the economy (from neutral and investment specific technology)')
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mu_I (long_name='growth rate of investment-specific technology growth')
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mu_A (long_name='growth rate of neutral technology')
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lambda (long_name='Lagrange multiplier')
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R (long_name='Nominal Interest rate')
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PI (long_name='Inflation')
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r (long_name='rental rate of capital')
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x (long_name='investment')
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u (long_name='capacity utilization')
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q (long_name='Tobin marginal q')
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f (long_name='variable for recursive formulation of wage setting')
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ld (long_name='aggregate labor demand')
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w (long_name='real wage')
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wstar (long_name='optimal real wage')
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PIstarw (long_name='optimal wage inflation')
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PIstar (long_name='optimal price inflation')
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g1 (long_name='variable 1 for recursive formulation of price setting')
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g2 (long_name='variable 2 for recursive formulation of price setting')
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yd (long_name='aggregate output')
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mc (long_name='marginal costs')
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k (long_name='capital')
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vp (long_name='price dispersion term')
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vw (long_name='wage dispersion term')
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l (long_name='aggregate labor bundle')
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phi (long_name='labor disutility shock')
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F (long_name='firm profits')
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;
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varexo epsd epsphi epsmu_I epsA epsm;
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varexo epsd (long_name='Innovation preference shock')
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epsphi (long_name='Innovation labor disutility shock')
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epsmu_I (long_name='Innovation investment-specific technology')
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epsA (long_name='Innovation neutral technology')
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epsm (long_name='Innovation monetary policy shock')
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;
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predetermined_variables k;
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parameters h //consumption habits
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betta //discount factor
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gammma1 //capital utilization, linear term
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gammma2 //capital utilization, quadratic term
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delta //depreciation rate
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kappa //capital adjustment costs parameter
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eta //elasticity of substitution between labor varieties
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epsilon //elasticity of substitution between goods varieties
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varpsi //labor disutility parameter
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gammma //inverse Frisch elasticity
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chiw //wage indexation parameter
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chi //price indexation
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thetap //Calvo parameter prices
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thetaw //Calvo parameter wages
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alppha //capital share
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Rbar //steady state interest rate
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PIbar //steady state inflation
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gammmaR //interest smoothing coefficient Taylor rule
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gammmaPI //feedback coefficient to inflation monetary policy rule
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gammmay //feedback coefficient to output growth deviation in monetary policy rule
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Phi //firms fixed costs
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rhod //autocorrelation preference shock
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rhophi //autocorrelation labor disutility shock
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Lambdamu //steady state growth rate of investmentment-specific technology
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LambdaA //steady state neutral technology growth
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Lambdax //steady state growth rate of investment
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LambdaYd //steady state growth rate of output
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sigma_d //standard deviation preference shock
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sigma_phi //standard deviation labor disutility shock
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sigma_mu //standard deviation investment-specific technology
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sigma_A //standard deviation neutral technology
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sigma_m; //standard deviation preference shock
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parameters h (long_name='consumption habits')
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betta (long_name='discount factor')
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gammma1 (long_name='capital utilization, linear term')
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gammma2 (long_name='capital utilization, quadratic term')
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delta (long_name='depreciation rate')
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kappa (long_name='capital adjustment costs parameter')
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eta (long_name='elasticity of substitution between labor varieties')
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epsilon (long_name='elasticity of substitution between goods varieties')
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varpsi (long_name='labor disutility parameter')
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gammma (long_name='inverse Frisch elasticity')
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chiw (long_name='wage indexation parameter')
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chi (long_name='price indexation')
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thetap (long_name='Calvo parameter prices')
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thetaw (long_name='Calvo parameter wages')
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alppha (long_name='capital share')
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Rbar (long_name='steady state interest rate')
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PIbar (long_name='steady state inflation')
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gammmaR (long_name='interest smoothing coefficient Taylor rule')
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gammmaPI (long_name='feedback coefficient to inflation monetary policy rule')
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gammmay (long_name='feedback coefficient to output growth deviation in monetary policy rule')
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Phi (long_name='firms fixed costs')
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rhod (long_name='autocorrelation preference shock')
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rhophi (long_name='autocorrelation labor disutility shock')
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Lambdamu (long_name='steady state growth rate of investmentment-specific technology')
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LambdaA (long_name='steady state neutral technology growth')
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Lambdax (long_name='steady state growth rate of investment')
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LambdaYd (long_name='steady state growth rate of output')
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sigma_d (long_name='standard deviation preference shock')
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sigma_phi (long_name='standard deviation labor disutility shock')
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sigma_mu (long_name='standard deviation investment-specific technology')
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sigma_A (long_name='standard deviation neutral technology')
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sigma_m (long_name='standard deviation monetary policy shock')
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;
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//Note that the parameter naming in FV(2010) differs from FV(2006)
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//Fixed parameters, taken from FV(2010), Table 2, p. 37
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@ -177,60 +182,67 @@ FV(2006), p. 20, section 3.2.
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*/
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model;
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//1. FOC consumption
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[name='FOC consumption']
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d*(c-h*c(-1)*mu_z^(-1))^(-1)-h*betta*d(+1)*(c(+1)*mu_z(+1)-h*c)^(-1)=lambda;
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//2. Euler equation
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[name='Euler equation']
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lambda=betta*lambda(+1)*mu_z(+1)^(-1)/PI(+1)*R;
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//3. FOC capital utilization
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[name='FOC capital utilization']
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r=gammma1+gammma2*(u-1);
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//4. FOC capital
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[name='FOC capital']
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q=betta*lambda(+1)/lambda*mu_z(+1)^(-1)*mu_I(+1)^(-1)*((1-delta)*q(+1)+r(+1)*u(+1)-(gammma1*(u(+1)-1)+gammma2/2*(u(+1)-1)^2));
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//5. FOC investment
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[name='FOC investment']
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1=q*(1-(kappa/2*(x/x(-1)*mu_z-Lambdax)^2)-(kappa*(x/x(-1)*mu_z-Lambdax)*x/x(-1)*mu_z))
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+betta*q(+1)*lambda(+1)/lambda*mu_z(+1)^(-1)*kappa*(x(+1)/x*mu_z(+1)-Lambdax)*(x(+1)/x*mu_z(+1))^2;
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//6-7. Wage setting
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[name='Wage setting 1']
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f=(eta-1)/eta*wstar^(1-eta)*lambda*w^eta*ld+betta*thetaw*(PI^chiw/PI(+1))^(1-eta)*(wstar(+1)/wstar*mu_z(+1))^(eta-1)*f(+1);
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[name='Wage setting 2']
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f=varpsi*d*phi*PIstarw^(-eta*(1+gammma))*ld^(1+gammma)+betta*thetaw*(PI^chiw/PI(+1))^(-eta*(1+gammma))*(wstar(+1)/wstar*mu_z(+1))^(eta*(1+gammma))*f(+1);
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//8-10. firm's price setting
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[name='Firm price setting 1']
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g1=lambda*mc*yd+betta*thetap*(PI^chi/PI(+1))^(-epsilon)*g1(+1);
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[name='Firm price setting 2']
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g2=lambda*PIstar*yd+betta*thetap*(PI^chi/PI(+1))^(1-epsilon)*PIstar/PIstar(+1)*g2(+1);
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[name='Firm price setting 3']
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epsilon*g1=(epsilon-1)*g2;
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//11-12. optimal inputs
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[name='Optimal capital labor ratio']
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u*k/ld=alppha/(1-alppha)*w/r*mu_z*mu_I;
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[name='Marginal costs']
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mc=(1/(1-alppha))^(1-alppha)*(1/alppha)^alppha*w^(1-alppha)*r^alppha;
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//13. law of motion wages
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[name='law of motion wages']
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1=thetaw*(PI(-1)^chiw/PI)^(1-eta)*(w(-1)/w*mu_z^(-1))^(1-eta)+(1-thetaw)*PIstarw^(1-eta);
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//14. law of motion prices
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[name='law of motion prices']
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1=thetap*(PI(-1)^chi/PI)^(1-epsilon)+(1-thetap)*PIstar^(1-epsilon);
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//15. Taylor Rule
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[name='Taylor Rule']
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R/Rbar=(R(-1)/Rbar)^gammmaR*((PI/PIbar)^gammmaPI*((yd/yd(-1)*mu_z)/exp(LambdaYd))^gammmay)^(1-gammmaR)*exp(epsm);
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//16-17. Market clearing
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[name='Resource constraint']
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yd=c+x+mu_z^(-1)*mu_I^(-1)*(gammma1*(u-1)+gammma2/2*(u-1)^2)*k;
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[name='Aggregate production']
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yd=(mu_A*mu_z^(-1)*(u*k)^alppha*ld^(1-alppha)-Phi)/vp;
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//18-20. Price and wage dispersion terms
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[name='Aggregate labor market']
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l=vw*ld;
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[name='LOM Price dispersion term']
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vp=thetap*(PI(-1)^chi/PI)^(-epsilon)*vp(-1)+(1-thetap)*PIstar^(-epsilon);
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[name='LOM Wage dispersion term']
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vw=thetaw*(w(-1)/w*mu_z^(-1)*PI(-1)^chiw/PI)^(-eta)*vw(-1)+(1-thetaw)*(PIstarw)^(-eta);
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//21. Law of motion for capital
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[name='Law of motion for capital']
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k(+1)*mu_z*mu_I-(1-delta)*k-mu_z*mu_I*(1-kappa/2*(x/x(-1)*mu_z-Lambdax)^2)*x=0;
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//22. Profits
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[name='Profits']
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F=yd-1/(1-alppha)*w*ld;
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//23. definition optimal wage inflation
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[name='definition optimal wage inflation']
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PIstarw=wstar/w;
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//exogenous processes
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//24. Preference Shock
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[name='Preference Shock']
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log(d)=rhod*log(d(-1))+epsd;
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//25. Labor disutility Shock
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[name='Labor disutility Shock']
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log(phi)=rhophi*log(phi(-1))+epsphi;
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//26. Investment specific technology
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[name='Investment specific technology']
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log(mu_I)=Lambdamu+epsmu_I;
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//27. Neutral technology
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[name='Neutral technology']
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log(mu_A)=LambdaA+epsA;
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//28. Defininition composite technology
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[name='Defininition composite technology']
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mu_z=mu_A^(1/(1-alppha))*mu_I^(alppha/(1-alppha));
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end;
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